Recursion:
def minimumNumberOfCoins(coins,numberOfCoins,value):
    
    def recur(coins, n, value):
        
        if n == 0:
            return float("inf")
            
        if value == 0:
            return 0
            
        if coins[n-1] > value:
            return recur(coins, n-1, value)
        else:
            return min(1 + recur(coins, n, value-coins[n-1]), recur(coins, n-1, value))
            
    res = recur(coins,numberOfCoins,value)
    
    if res == float("inf"):
        return 0
    return res

Bottom Up:
def coinChange(coins, amount):
        
    n = len(coins)
    
    def recur(amount,coins,n,dp):
        
        if dp[n][amount] != -1:
            return dp[n][amount]

        if coins[n-1] > amount:
            dp[n][amount] =  recur(amount,coins,n-1,dp)

        if coins[n-1] <= amount:
            dp[n][amount] =  min(1 + recur(amount - coins[n-1],coins,n,dp), recur(amount,coins,n-1,dp))
        
        return dp[n][amount]
        
    dp = [[-1 for i in range(amount+1)] for j in range(n+1)]
    

    for i in range(amount+1):
        dp[0][i] = float("inf")
    
    for i in range(1, n+1):
        dp[i][0] = 0

    recur(amount,coins,n,dp)
    
    if dp[n][amount] == float("inf"):
        return -1
    return dp[n][amount]

Top Down:
def coinChange(coins, amount):
    n = len(coins)
    def recur(amount,coins,n,dp):
        
        for i in range(1, n+1):
            for j in range(1, amount+1):
                
                if coins[i-1] > j:
                    dp[i][j] = dp[i-1][j]
                else:
                    dp[i][j] = min(1 + dp[i][j-coins[i-1]], dp[i-1][j])
                    
    dp = [[-1 for i in range(amount+1)] for j in range(n+1)]
    

    for i in range(1, amount+1):
        dp[0][i] = float("inf")
    
    for i in range(n+1):
        dp[i][0] = 0
        
    recur(amount,coins,n,dp)
    
    if dp[n][amount] == float("inf"):
        return -1
    return dp[n][amount]